This is (of course) a growing list:
Burgin. “A new elementary proof of Landau’s prime ideal theorem, and associated results.” Res. Number Theory(2025)11:28 https://doi.org/10.1007/s40993-025-00617-x https://arxiv.org/abs/2406.08565
Burgin, Keleti, Goldberg, MacMahon & Wang. “Large sets avoiding infinite arithmetic / geometric progressions.” Real Analysis Exchange, 2023. https://arxiv.org/abs/2210.09284
Burgin. “The Schrodinger Maximal Function and Generalizations.” Senior thesis at Duke under Lillian Pierce, 2023. Available upon request.